Question

What is a system of equations for the following situation? There is a total of 40 questions on a test. Some questions are multiple-choice and some are short answers. The multiple-choice questions are worth 2 points and the short answer questions are worth 4 points. There is a total of 100 points on the test.

Answer 1

First we define the variables:

m = multiple choice questions

s = short answer questions

Next we need to satisfy 2 conditions:

1) There are a total of 40 questions. We can represent this mathematically using the variables I defined:

$m+s=40$

2) The multiple-choice questions are worth 2 points and the short-answer are worth 4 points but they need to total 100 points. This can also be represented mathematically:

$2m+4s=100$

By satisfying the conditions provided we were able to create the 2 equations!

$m+s=40$

$2m+4s=100$